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A316074
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Sequence a_k of column k shifts left k places under Weigh transform and equals signum(n) for n<k; triangle T(n,k), n>=1, 1<=k<=n, read by rows.
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13
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1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 1, 6, 2, 2, 1, 1, 1, 12, 4, 2, 2, 1, 1, 1, 25, 6, 3, 2, 2, 1, 1, 1, 52, 10, 5, 3, 2, 2, 1, 1, 1, 113, 17, 7, 4, 3, 2, 2, 1, 1, 1, 247, 29, 10, 6, 4, 3, 2, 2, 1, 1, 1, 548, 51, 17, 8, 5, 4, 3, 2, 2, 1, 1, 1, 1226, 89, 26, 12, 7, 5, 4, 3, 2, 2, 1, 1, 1
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OFFSET
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1,7
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LINKS
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M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
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EXAMPLE
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Triangle T(n,k) begins:
1;
1, 1;
1, 1, 1;
2, 1, 1, 1;
3, 2, 1, 1, 1;
6, 2, 2, 1, 1, 1;
12, 4, 2, 2, 1, 1, 1;
25, 6, 3, 2, 2, 1, 1, 1;
52, 10, 5, 3, 2, 2, 1, 1, 1;
113, 17, 7, 4, 3, 2, 2, 1, 1, 1;
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MAPLE
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b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(binomial(T(i, k), j)*b(n-i*j, i-1, k), j=0..n/i)))
end:
T:= (n, k)-> `if`(n<k, signum(n), b(n-k$2, k)):
seq(seq(T(n, k), k=1..n), n=1..16);
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MATHEMATICA
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b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0, Sum[Binomial[T[i, k], j]*b[n - i*j, i - 1, k], {j, 0, n/i}]]];
T[n_, k_] := If[n < k, Sign[n], b[n - k, n - k, k]];
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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